## Table of content

The modern world is full of opportunities and a plethora of options. While one is now unrestricted to conventional forms of learning based on dated mechanisms and techniques, it can also lead to immense confusion among students. Understanding all the available options is essential to make a sound decision. Now, educational institutes like schools and colleges provide an abundance of different streams and courses to choose from. With the ever-changing dynamics of the modern world, education curriculums have adopted a different approach and brought on new insights while designing their modules for students of all ages. One such board is International Baccalaureate. Formulated in October 1968, the I.B. Board is affiliated with 4,460 schools globally. I.B. Board seeks to provide legal education to children internationally, along with practical learning through life experiences. It further promotes a more interactive and student-centric approach. By delivering consistent education to students from ages three to nineteen, it focuses on the overall enhancement of its students.

The I.B. Board is divided into three curricula for different age groups: the Primary Years Programme (PYP), which makes children of ages 3 to 12, making them active participants in the learning process; Secondly, the Middle Years Programme (MYP), students between 12 to 16 years of age. This programme aims to challenge young minds and help make practical associations between their academics and the real world.

The programme that concerns us the most and one of which I.B. Maths is part of the International Baccalaureate (I.B.) Diploma Programme. This program is tailored to suit the intellectual and academic needs of students between 16 to 19 years of age.

## What Comes Under The IB Diploma Programme?

The curriculum of the two-year course involves students completing six studies chosen from the six diverse subject groups. They are required to complete one extended essay, which involves a self-directed, independent research project along with a theory of knowledge course and get a chance to participate in creativity, activity and service projects.

The s**ix subject group**s within the Diploma Programme are

- Studies in Language and Literature
- Language Acquisition
- Individuals and Societies
- Sciences
- Mathematics
- Arts

There are different courses under each subject group, and students can design their own curriculum. Furthermore, they are free to choose the course of a standard level or the higher level depending on their past studies and learning needs, as well as their university preference. Both groups contrast in their scope but are validated by the same grade descriptors. However, the higher level demands an elevated understanding of concepts and skills. Each student must take three higher-level courses, the rest at the standard level. The average level comprises 150 hours of teaching, whereas the higher level requires 240 hours.

## Association Of IB Maths With Middle Years Programme

Students continue to build their mathematical knowledge and skills when they transfer from the Middle Years Programme to the Diploma Programme or the Career-related Programme (CP). This subsequently enables them to pursue studies in a broad range of subjects. The MYP and the DP place a strong emphasis on inquiry-based learning, giving students a chance to individually and jointly study, solve problems, and articulate their mathematics at more sophisticated levels.

The objectives of the MYP mathematics and DP mathematics courses are strikingly similar. The MYP mathematics guide has been used with the initial learning concepts for developing DP mathematics courses. The DP mathematics course principles are connected with the framework of essential images used in the MYP courses. These ideas are broad, robust, regulating and relevant to the subject at hand and other subject areas. Students who take DP mathematics courses benefit significantly from the principal factors of MYP mathematics, as it also helps them with their future studies.

The DP's internal and external assessment requirements have been considered when formulating the MYP mathematics assessment objectives and criteria. One of the four MYP assessment objectives for mathematics students is to practise and strengthen their inquisitive abilities; this is an essential foundation for the DP mathematics courses' internal assessment component. The higher-order assessment goals of communication and interpretation, as well as reasoning, that are required of DP math students, are aligned with the MYP assessment goal of critical thinking. Both courses extensively encourage using technology as an instrumental tool in learning and for the application and communication of mathematics. Technology, therefore, plays a principal role in this.

In contrast to the MYP, where students may choose between standard and extended mathematics, the DP offers two mathematics courses available at the SL and HL levels. Students in the MYP taking illustrative math typically decide to enrol in one of the HL math courses in the DP. When choosing which Standard Level or Higher Level course is ideal for them to study, MYP-level mathematics students should ask their teacher for advice and conduct thorough research themselves, keeping all the extended factors in mind.

## IB MATHS: Options And Details

Mathematics is a subject of logic and hard-proven facts and concepts. It is often described as a study of structure, order and relation, which has evolved from inspecting, counting, measuring and describing objects.

One side of mathematics is driven by abstraction and generalization; it is drawn out of ideas and provides a new perspective by linking these ideas to new emerging ones. Such statements and concepts may no longer hold a prominent place in the practical world but studying them helps students expand their knowledge and builds a secure foundation. Another relatively new facet of maths is built upon theorems, axioms, and logical-mathematical principles; The study of this side of maths is usually concerned with studying another subject. Mathematics is used in numerous disciplines as a language or an instrument to explore universal phenomena. Its application lies in making predictions and foreseeing risks.

While these two elements of maths seem to be unrelated, they are integrated with each other. The two courses available under the Diploma Programme of the International Board explore the differences in two aspects of maths and the features that connect them. Their approaches toward maths may be based on different perspectives, but their basis is grounded in the same mathematical methodology, concepts and techniques for problems and the respective solutions.

The options available within IB Mathematics are

- Mathematics: Analysis and Approaches;
- Mathematics: Applications and Interpretation

They are both offered at Standard Level as well as at the Higher Level. This distinction between the two accommodates and satisfies the student's needs, interests, desires and abilities. It seeks to suit all types of students; For those who wish to pursue knowledge of maths as a subject in its own right or to explore different topics related to maths and those who have the desire to study maths in a larger context by connecting it to the real world and its implications on the same. It proves of excessive importance for both.

## Difference between maths AA and maths IA:

Point of Difference | Maths AA | Maths IA |
---|---|---|

Objective of the course - | Development of extensive vigorous skills in mathematical thinking. | Strengthening of practical application knowledge of mathematics. |

Focal Point - | Algebraic methods and equations. | Emphasis on Modelling and Statistics. |

Aspects explored - | Mathematical questions and examining practical and theoretical applications. | Constantly experimenting with technology to tackle actual mathematical problems and have pragmatic solutions. |

Recommended for - | For students with a considerable interest in economics, engineering, and physical sciences. | For young adults with an interest in design thinking, business, engineering, statistics, the social sciences, the natural sciences, and medicine. |

## Mathematics: Analysis And Approaches

The Modern World is dependent on innovation and experiments. Following suit, this course acknowledges the need for a more excellent grasp of analytical expertise in mathematics.

## Motives Behind The Structure Of The Syllabus

The syllabus is based on a diversity of topics that are both parts of traditionally taught pre-university courses, such as trigonometry and calculus, along with issues that are susceptible to inspection, conjecture and corroboration.

This course tackles two separate yet equally essential realms of study within Mathematics. This course is open to the use of technology as it deems fluency in pertinent mathematical software and handheld technology of great value. It emphasizes the ability to formulate, communicate and account for valid mathematical arguments.

*The aims of the Diploma Programme Mathematics course are to aid students in*

- Inculcating curiosity and joy in maths, And acknowledging its power and sophistication.
- Aiding the students with their ability to clearly communicate mathematics concisely and, coherently; Confidently in varied contexts.
- Enabling students to develop an understanding of complex concepts, the nature of mathematics and its various principles.
- Helping students acquire the skill of refinement and application of abstraction and generalization.
- Developing creative and practical thinking and the skill to solve a problem with patience and precision, resulting in valuable confidence.
- Applying mathematics in logical circumstances and alternative situations, such as areas of knowledge and new developments in local and global communities.
- Acknowledgement and appreciation of the correlation between technology and mathematics.
- Value the moral, social and ethical questions from applications and working in mathematics.
- Gain admiration for the universality of maths and the ability to study it in its multicultural, social, international and historical contexts.
- Gain an appreciation for mathematics's influence in other fields, especially as an area of knowledge in IB's Token of Knowledge Course.
- Attain the skill to critically review their own work and others.'
- Through collaboration or personal efforts, they expand their knowledge of mathematics.

*Expectations of Students:*

- The course expects students to be efficient in the manipulation of algebraic expressions.
- They should be able to recognize distinct mathematical patterns and the generalization of the same.
- At the higher level, students should be comfortable handling complex algebraic equations and can understand the simple proof.

While the Higher LevelLevel in this course provides an extensive curriculum, it is recommended for people who are sure about pursuing mathematics in their respective university education as opposed to taking up Standard Level, which is more suited to the needs of students who aim to subjects that required mathematical backgrounds such as geography, economic and chemistry.

Apart from additional 90 hours to explore the subject comprehensively at a Higher Level, the topics taught remain unchanged at both levels, including Numbers and Algebra, Functions and Trigonometry, Probability and Statistics, and Calculus and Functions.

### Difference Between Standard Level and Higher Level Maths AA

SL & HL topics | Recommended hours (HL) | Recommended hours (SL) |
---|---|---|

Toolkit and Exploration | 30 | 30 |

Number and Algebra | 39 | 19 |

Geometry and Trigonometry | 51 | 25 |

Calculus | 55 | 28 |

Functions | 32 | 21 |

### Difference Between Standard Level and Higher Level Maths AA

Topics | Standard level (SL) | Higher level (HL) |
---|---|---|

Number and Algebra | Arithmetic and geometric sequences, series and their applications including laws of logarithms and exponentials, solving exponential equations, simple proof, approximations and errors, binomial theorem and scientific notation. | Permutation and combination, partial fractions, complex numbers, proof by induction, contradiction and counter-example, solution of systems of linear equation. |

Statistics and Trigonometry | It involves data collection making use of sampling techniques, measures of central tendency and spread, probability diagrams, correlation, regression, normal distribution with variable standards, binomial distribution, and probability calculations. | Probability density functions, Bayes Theorem, Bayesian inference, and expectation algebra. |

Functions | Straight line equations, ideas and characteristics of functions, and their graphs, including composite, inverse, identity, rational, exponential, logarithmic, and quadratic functions. | Rational functions, odd and even functions, self-inverse functions, solving function inequalities, factor and remainder theorems, sums and products of polynomial roots, and the modulus function. |

Calculus | Informal concepts of limits and convergence, a differentiation that takes into account the graphical behaviour of functions, the discovery of normal and tangent equations, optimisation, kinematics that includes displacement, velocity, acceleration, and the total distance travelled, the chain, product, and quotient rules, and definite and indefinite integration. | Basics to continuity and differentiability, convergence and divergence, differentiation from first principles, limits and L'Hopital's rule, implicit differentiation, derivatives of reciprocal and inverse trigonometric functions, integration by substitution and parts, volumes of revolution, and first-order differential equations solution using Euler's method by separating variables and using the integrating factor, Maclaurin series. |

Geometry and Trigonometry | Volume and surface of three-dimensional solids, right-angled and non-right-angled trigonometry, radian measurement, the unit circle and the Pythagorean identity, the double angle identity for sine and cosine, composite trigonometric functions, and solving trigonometric equations are all covered. | Vector theory, use with lines and planes, reciprocal trigonometric ratios, inverse trigonometric functions, compound angle identities, double angle identities for tangents, symmetry characteristics of trigonometric graphs, and vector algebra. |

## Maths AA Assessment Model

Acquiring mathematical skills and concepts in various contexts, including unconventional, open-ended, and practical problems is central to learning conventional mathematics syllabi.

__- Knowledge and understanding:__

This involves recall, selection and application of proven mathematical facts, ideas, and methods in a wide range of unexpected or expected situations. This list of objectives is formulated to enable students to test their application skills in the exploration project, where they are allowed to follow their personal interests without any external pressure or time constraint.

__- Problem-solving:__

Learning, selecting and applying one's arithmetical skills, outcomes, and models to problems of both abstract and concrete nature.

__- Communication and interpretation:__

Employ mathematics in standard real-world settings; remark on the ground; sketch or use technology to create mathematical diagrams, graphs, or constructions; use the standard notation to record the methods, solutions, and conclusions; utilize appropriate terminology and notation.

__Technology:__

Utilizing technology correctly, appropriately, and effectively to investigate novel concepts and resolve issues. Finding new and practical uses of technology, along with mathematics.

__Reasoning:__

Utilizing precise statements, logical deduction and inference, manipulating mathematical expressions to construct mathematical arguments, and working on their implementation.

__Inquiry approaches:__

Investigating familiar situations, both abstract and real-world issues, through organizing and evaluating data, making hypotheses, testing hypotheses' validity, and so on.

## Internals: Breaking Down The Exploration

The Mathematics Internal assessment forms 20% of the total grade for Mathematical studies, Standard or Higher Level. For this Assessment, the student is required to write a Mathematical Exploration Paper on the topic of their choice. The International Bacculate Board recommends it to be 6-12 pages long depending upon the subject and content along with the level of maths which corroborates with the difficulty of the course. This can also include topics studied within the syllabus, but it is highly recommended to look beyond the scope of the curriculum. It is also plausible to select the case from the optional module available at the Higher Level to avoid studying for potential starting points.

## Marking Criteria

The marking criteria are split into five categories— communication, mathematical representation, reflection, personal engagement and use of mathematics.

*Communication:*

This category carries four marks and refers to clear, concise, coherent and well-presented communication in the internal assessment. Consciousness has been the main focus of the IB Board, as it strictly recommends for the assignments be six to twelve pages in length. It has also been recognized through past papers that discursive term draws away from the quality of the student's work. Furthermore, it is also proposed that all graphical representations, such as tables, charts, and other things, should be included in the body. This provides clarity and an incredible opportunity to score better marks. Citations and Bibliography hold the most critical place, ensuring that you steer clear of plagiarism.

*Mathematical Presentation:*

This aspect of IA makes up for 3 marks in the final calculations. Primarily IBO recommends that the keywords are highlighted in every case. All definitions found in journals and textbooks and referred to in the article can enhance the essay's quality and aid the examiner in exploring and understanding the topic better. It is also imperative to use meticulous mathematical language such as symbols, terminology, and notations; however, it is also advised to be clear in your language, as if misused, it could potentially have negative implications on your scoring. It could also lead the examiner to assume that there needs to be more understanding.

Moreover, making your presentation visually appealing reaps good marks. Please write your own equations and graphs( you can use different apps to remove branding) and ensure each has axes labels and titles. Last but not least, make sure every chart has a purpose. Doing so will exhibit an ability to draw out critical analyses and present your equations coherently and concisely.

*Personal Engagement:*

This aspect of the internal assignment holds 4 marks in the final evaluation. Often considered the trickiest criteria of the five requires a demonstration of the connection between the topic and the personal life.

While fulfilling this criterion, here are a few things that one should keep in mind-

- Ensure that you use the First Person's Narrative. This will reflect your interest and credibility of the project you have worked on.
- Use a distinct approach to present your exploration to differentiate your work from other students and represent originality instead of just using a template approach.
- Please discuss your difficulties while working on your project and your experiences. This will also boost your score in personal engagement and reflection criteria.
- Discussing your downs and lows while progressing in your exploration would also add to the personal engagement of your presentation and would work to translate your experiences well.
- Most importantly, it would help if you accentuated what you gained through this exploration and how your past learnings, in the context of this course, have enabled you to carry forward this project. Make sure to highlight all your mathematical concepts.

*Reflection:*

Reflection carries three marks in the overall evaluation. IB does not encourage their students to work on an exploration that always yields the right or desired results; instead, it encourages students to take a firm stance that through the investigation, stumbling upon unexpected or supposedly wrong results is not necessarily a bad thing; It sees it as an opportunity to grow and learn from the process and analyze where you went wrong thereby giving its student a chance to reflect on their work. Recognizing where your exploration went wrong and how it can be fixed is essential. Simultaneously, it is of the utmost importance to reflect on the successes of your inquiry, especially on the elements you were able to prove. In this aspect, discussing the weaknesses and strengths of your project will aid you in obtaining a top score.

Moreover, consider the approaches you took and the ones you could have taken and how they would have created a difference in your research. (For example, did you build your complex exploration over the base of a simple model allowing you to isolate certain vital equations?) The ability to evaluate potential approaches will represent your superior and critical analysis. Based on the amount of space left, you could also discuss how your work could become instrumental in further explorations and how they could further help develop an understanding of current topics.

*Use of Mathematics:*

This aspect is the most significant percentage of the final evaluation, with 6 marks. Unlike the general presumption, one does not have to go beyond the scope to score high marks. Still, according to International Baccalaureate, one should instead use mathematics commensurate with the level of your course. This does not mean sticking to only the subject in the syllabus but taking it and exploring it beyond what the system offers. Alternatively, you can use basic information in a new scenario. Make sure to leave some space for "creativity or personalized problem" to score on the personal engagement front.

This is the fifth and last end of our criteria for the internal assessment. One crucial factor to note is to remember that IB is concerned with depth of knowledge and understanding of the chosen topic; therefore, mathematics can be simple but significantly well-explored.

## Mathematics AA And Theory Of Knowledge

The integration of each subject with the values of Token for Knowledge is a fundamental part of the International Baccalaureate Diploma Programme. The Theory of Knowledge course motivates the students to introspect their pre-conceived notions and presumptions in order to help them become completely aware of their own and others’ perceptions. Comprehensively, this aids them to become inquiring, knowledgeable and caring young people. It seeks to provide a platform for students to question how knowledge is fabricated and shared, both in maths and across different disciples. The application of knowledge becomes pragmatic and has it go beyond academia.

What makes mathematics distinctive from other subjects is the certainty that it secures in any situation. In The Theory of Knowledge, students are motivated to study the growing tensions and relationships relating to the knowledge of mathematics. Mathematics is simultaneously providing important information about the world and new fronts in science and technology leading force that propels scientific progress. The Theory of Knowledge draws the student's attention towards questions such as whether mathematical knowledge actually exists independently beyond our thinking of it.

## Mathematics AA & International Mindedness

An openness to the world and a knowledge of our profound interconnectedness with others are two characteristics that define international-mindedness and a style of thinking, being and acting. The global exchange of mathematical information and knowledge has withstood the influx of upcoming information and communication technologies and has been indispensable in the development of mathematics.

Encompassing various metrics, mathematics can be compared to a universal language, and mathematicians worldwide can clearly articulate within their discipline despite minor differences in notation. Great civilizations throughout history have owed part of their success to their mathematicians' ability to build and maintain complex social and architectural institutions. Mathematics can transcend politics, religion, and ethnicity. Politics has heavily shaped the growth of mathematics, ballistics, navigation, trade, and land ownership, often with the help of authorities and leaders. Many early mathematicians served as military and political analysts, and today mathematicians are an essential part of teams advising governments on allocating funds and resources.

Although it may not always be obvious, mathematics, the language of science, is a crucial part of most technological innovations and supports breakthroughs in science and technology. Offering opportunities for research into various regional and international topics and concepts is one method of fostering international-mindedness. Multiple global organizations and bodies presently promote mathematics, and students are encouraged to use their materials and frequently sizeable websites. This can broaden their understanding of the global nature of mathematics and give them more chances to interact with worldwide problems associated with the field.

## Mathematics AA in Reference to Creativity, Activity And Service (CAS)

There are several ways that CAS and mathematics can complement one another. Mathematical knowledge offers a crucial key to comprehending the world's reality. The mathematical abilities and procedures students learn in mathematics courses will empower them to assess the environment, enabling them to create, organize, and present CAS experiences or various projects.

Students with a coherent understanding of how mathematics can be used to demonstrate the truth are better equipped to analyze the information that societies obtain or generate and how this affects the distribution of resources or the decisions individuals make. Students' capacity to investigate issues methodically and their ability to identify how mathematics might affect the world around them are both key outcomes of mathematics courses. This meticulous analysis and analytical problem-solving offer motivating baselines for CAS projects.

## Do Universities Prefer Maths AA Or AI?

While many universities do not have a prerequisite for a particular maths course, some universities might weigh Maths AA at a higher level than Maths IA and vice versa. Much of this preference also depends on the subject you wish to pursue in higher studies.

### Below Is a List of Universities in Terms of Their Expected Course in IB Mathematics (This list was last Updated in 2019, it is Advisable That you Should Double Check the Subject Preferences With the College Counsellor so as to not Miss any Changes)

University: | Preference of Maths AA: | Respective Courses: |
---|---|---|

Bristol University, United Kingdom | No (Requires Higher Levels in Mathematics) | - |

Cambridge University, United Kingdom | Yes | Any course with a requirement of Maths |

Exeter University, United Kingdom | Yes (Higher Level only) | Engineering, Maths, Computer Science and Natural Science degrees |

German Universities | Either Course with Higher Level | |

Imperial College, United Kingdom | Yes | Physics |

King’s College London | Yes | Mathematics ( all course), Physics (all course, Engineering (all Biomedical and Electronic programmes) |

London School of Economics | Yes | BSc Economics, BSc Finance |

McGill Canada | No (Requires Higher Level in Maths-IA) | - |

Oxford University | No | - |

Swiss Universities | No | |

University of Toronto | No (Requires Higher Level in Maths-IA) | Science and Business programs |

University College London | Yes | Programmes requiring further mathematics at A-level |

Warwick University | Yes | Mathematics, Physics, Computer Science |

Webster University | No | - |

University of Bath | Yes | Mathematics, Physics, Computer Science, Economics |

Sussex UK | No (Requires HL in Maths) | - |

ESCP- Europe Business School | Yes (Higher Level only) | - |

Concordia Canada | No | - |

What should you keep in mind **choosing your course?**

There are three major things one should keep in mind while making this decision-

- Your skill, abilities and passion and their co-relation to diverse areas within mathematics.
- How does combining your chosen subjects complement your course and future aspirations?
- Students' future academic and career aspirations and how your course helps them in their path towards it.
- IBO recommends Maths AA for students aspiring to pursue a future in Mathematics, Physical Sciences, Engineering and Economics.

If students are still dubious, it is crucial to keep in mind Georg Cantor's statement: "*the essence of mathematics is in its freedom*." It is imperative to follow one's passion in today's age because there are numerous options for any path you decide to take that lead to places of utmost fulfilment. Students should opt for a course that resonates with them the strongest with their beliefs and to know that the art of framing the question should be held in higher regard than solving it.

Eventually, it will fundamentally matter and helps you score and advance further in life; And; therefore, choosing the course you are interested in will ensure that you give it your all and even if you run into any obstacles, you'll always be determined to work them out.